I've yet to see anyone claim it means what you just wrote. When talking about scriptural (almost always Old Testament) events, I've only seen it used to say that some of the events surrounding a particular historical person as narrated in the OT may not have literally happened as described.

There are hundreds of places in the scriptures in which the phrase "the face of the whole earth" is used in a manner that clearly means a specific geographical location. Yet, if someone suggests that the same phrase in reference to a big flood might also mean something such as "known world" or "local region" as it does in other scripture passages, then it's amazing how many appear to call blasphemy on it.